To make the marinade, combine all the ingredients in a shallow 14-inch glass baking dish and stir until the honey is dissolved. Add the flank steaks and turn to coat with the marinade. Cover and refrigerate overnight.

Bring the steaks to room temperature. Prepare coals for grilling or preheat the broiler. Drain the steaks, reserving the marinade. Place the marinade in a large skillet and bring to a boil over high heat. Continue boiling until the liquid is syrupy and mahogany-colored, about 10 minutes. Remove from the heat and let cool. (There should be about 1 cup of glaze.)

Brush the glaze on both sides of the steaks. Grill or broil the steaks 4 inches from the heat until nicely glazed, about 5 minutes. Turn and grill or broil 5 minutes longer for medium-rare steaks. Let the meat rest for 5 minutes before carving.

Transfer the steaks to a cutting board. If you broiled the steaks, reserve any pan drippings. Holding a sharp knife at a 45-degree angle, cut the steaks across the grain into thin slices. Transfer the meat to a warmed platter, top with the pan drippings, and serve immediately.